slarra (l) - Linux Man Pages

slarra: the splitting points with threshold SPLTOL

NAME

SLARRA - the splitting points with threshold SPLTOL

SYNOPSIS

SUBROUTINE SLARRA(
N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO )

    
IMPLICIT NONE

    
INTEGER INFO, N, NSPLIT

    
REAL SPLTOL, TNRM

    
INTEGER ISPLIT( * )

    
REAL D( * ), E( * ), E2( * )

PURPOSE

Compute the splitting points with threshold SPLTOL. SLARRA sets any "small" off-diagonal elements to zero.

ARGUMENTS

N (input) INTEGER
The order of the matrix. N > 0.
D (input) REAL array, dimension (N)
On entry, the N diagonal elements of the tridiagonal matrix T.
E (input/output) REAL array, dimension (N)
On entry, the first (N-1) entries contain the subdiagonal elements of the tridiagonal matrix T; E(N) need not be set. On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT, are set to zero, the other entries of E are untouched.
E2 (input/output) REAL array, dimension (N)
On entry, the first (N-1) entries contain the SQUARES of the subdiagonal elements of the tridiagonal matrix T; E2(N) need not be set. On exit, the entries E2( ISPLIT( I ) ), 1 <= I <= NSPLIT, have been set to zero SPLTOL (input) REAL The threshold for splitting. Two criteria can be used:
SPLTOL<0 : criterion based on absolute off-diagonal value
SPLTOL>0 : criterion that preserves relative accuracy TNRM (input) REAL The norm of the matrix.
NSPLIT (output) INTEGER
The number of blocks T splits into. 1 <= NSPLIT <= N.
ISPLIT (output) INTEGER array, dimension (N)
The splitting points, at which T breaks up into blocks. The first block consists of rows/columns 1 to ISPLIT(1), the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), etc., and the NSPLIT-th consists of rows/columns ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
INFO (output) INTEGER
= 0: successful exit

FURTHER DETAILS

Based on contributions by

Beresford Parlett, University of California, Berkeley, USA
Jim Demmel, University of California, Berkeley, USA

Inderjit Dhillon, University of Texas, Austin, USA

Osni Marques, LBNL/NERSC, USA

Christof Voemel, University of California, Berkeley, USA